What is the value of x, given that PQ || BC?

Question

∆PAQ : PA = 6, AQ = x
∆BAC : BP = 12 , QC = 26

Answer 1

Since PQ || BC, we know that ∆PAQ and ∆BAC are similar. Therefore, their corresponding side lengths are proportional.

Using the side proportionalities, we can set up the following equation:

PA/AQ = BP/QC

Substituting the given values, we get:

6/x = 12/26

Cross-multiplying and simplifying, we obtain:

x = 13

Therefore, the value of x is 13.